MATH 1022 Chapter : Section 10 2
1
10.2 Graphing Polar Equations
OBJECTIVE 1: Sketching Equations of the Form
cosra=
,
sinra=
,
cos sinar br c+ =
, and
=
Graphs of Polar Equations of the Form
cosra=
,
sinra=
,
cos sinar br c+=
, and
=
where a, b, and c are constants.
Ex. 1: Sketch the graph of rcos θ = 5.
Identify graph:
Sketch the graph
The graph of cos is a vertical line.ra=
The graph of sin is a horizontal line.ra=
The graph of cos sin is a linera br c + =
with slope and intercept .
aa
my
bb
= − −
The graph of is a line through the pole that =
makes an angle of with the polar axis.
2
Ex. 2: Sketch the graph of 3r cos
- 4r sin
= -5
Identify graph:
Sketch the graph
OBJECTIVE 2: Sketching Equations of the Form
= = =, sin , and cosr a r a r a
and
=+cosr a b
Graphs of Polar Equations of the Form
=ra
,
=sinra
, and
=cosra
where
0a
is a constant
Ex. 3: Sketch the graph of the polar equation. r = -3 sin
Identify graph:
Sketch the graph
The graph of is a circlera=
The graph of sin is a circlera=
The graph of cos is a circlera=
centered at the pole with
a
centered on the line = that is units
22
a
from the pole with radius of length .
2
a
centered on the polar axis that is units
2
radius of length a .
a
from the pole with radius of length .
2
3
OBJECTIVE 3: Sketching Equations of the Form
=+sinr a b
and
=+cosr a b
Graphs of Polar Equations of the Form
=+sinr a b
and
=+cosr a b
where
0a
and
0b
are
constants.
1The graph is a cardioid if .
a
b=
The graph is a limacon with an inner loop if <1.
a
b
The graph is a limacon with a dimple if 1< <2.
a
b
The graph is a limacon with no inner loop and no dimple if 2.
a
b
Document Summary
R a = , sinr a = , ar cos br sin. = , and = c r a = , sinr a = , ar cos br sin. The graph of sin r a = is a horizontal line. r a = Objective 1: sketching equations of the form cos. Graphs of polar equations of the form cos where a, b, and c are constants. 1: sketch the graph of rcos = 5. Sketch the graph is a vertical line. sin br y. The graph of and with slope m intercept c is a line cos a ra a b b is a line through the pole that. The graph of makes an angle of with the polar axis. 2: sketch the graph of 3r cos - 4r sin = -5. Objective 2: sketching equations of the form = Graphs of polar equations of the form =r a , = sin.
